The Path to Success
SCHOOL OF MATHEMATICS Math Pathways Guide Use this guide to help you choose the correct math courses for your major. What is a Mathematics Pathway?
The mathematics pathway is a collection or sequence of mathematics courses offered in the School of Mathematics at Daytona State College. It offers clear direction from the program or Meta major to courses that are needed to meet the general education requirements.
This booklet will help you guide students through the mathematics pathways that are available to them at Daytona State. They can save time and money when students choose the right pathway. The School of Mathematics is eagerly waiting to assist them in their educational endeavors. What is a Jobs for Math Majors that Offer Awesome Opportunities Mathematics Some think jobs for math majors are only about crunching numbers in an ivory tower. Think again. Degrees can open the door to a huge range of amazing careers. After all, math is involved in just about Pathway? every job in some way, and it's particularly essential in the in-demand fields of science, technology, and engineering. If students have a solid grasp of math, jobs in many areas become more available to them. Math majors tend to have well-developed skills in logical thinking and problem solving.
We have assembled a list of entry-level jobs for math grads with a bachelor's degree as well as a few jobs that require more advanced training. This list is meant to inspire students' career exploration, but don't think students are limited to these suggestions. Many jobs that don't specifically mention math degrees are available to graduates with these skills, so don't sell the student short. They likely have more options than you realize.
Math Occupations Level Education Median Pay Job Outlook (2016–2026) Accountant Bachelor's $69,350 10% Actuaries Bachelor's $101,560 22% Aerospace Engineer Bachelor's $113,030 6% Biologist Bachelor's $62,290 8% Biomedical Engineer Bachelor's $88,040 7% Chemical Engineer Bachelor's $102,160 8% Civil Engineer Bachelor's $84,770 11% Computer Programming Bachelor's $82,240 -7% Enviornmental Engineer Bachelor's $86,800 8% Financial Manager Bachelor's $125,080 19% Forensic Science Technician Bachelor's $57,850 17% Geographer Bachelor's $76,860 7% Mechanical Engineer Bachelor's $85,880 9% Operations Research Analysts Bachelor's $81,930 27% Petroleum Engineers Bachelor's $132,280 15% Epidemiologists Master's $69,660 9% Mathematicians and Statisticians Master's $84,760 33% Physicist Ph.D. $117,220 14% Post-Secondary Teacher Ph.D. $76,600 15% On-Time 2 & On-Time 3 Classes Work (7-Week Sections)
The On-Time 2 and On-Time 3 graduation plans allow full-time students to focus on three courses at a time and part-time students to focus on two classes at a time and graduate within two or three years. In the On-Time 2 schedule, a student completes two A-term sections, one full-term section, and 2 B-term sections each semester to graduate in two years. In the On-Time 3 schedule, a student completes one course in A-term, in full-term, and in B-term each semester (plus one in each summer semester) to graduate in three years.
Short-term sections, particularly in mathematics or foreign language, frequently have higher success rates than those completed over the course of a full-term semester. We believe this is because mathematics is like a language where it is best learned if a student is immersed in the subject. To do math every day, or to speak a language every day, is the surest way for students to learn the material. In fact, data about success rates in short-term versus full-term semesters shows that in most cases students succeed at higher rates in short-term courses.
During the 2016-17 academic year, for example, students completing a full-term MGF2106 were successful 76% of the time during fall semester and 70% of the time during spring semester. But during the A-term semester, students were successful 80% of the time during fall semester and 93% of the time during the spring semester. The college also has data that breaks this down by students’ PERT score, which shows that on 14 measures, students did better in 10 of those instances. We encourage you to get them into these short-term courses to better help them succeed in their math courses! GET THERE FASTER! At DSC, we know a thing or two about how to help our students stay on track. Our On-Time Finish plans give you a clear path to get the right classes and graduate on time with your associate of arts university transfer degree. You decide whether you want to complete your degree in TWO years or THREE, depending on your life circumstances, and we’ll help you make sure it happens. ASK AN ACADEMIC ADVISOR TODAY!
Want to finish your degree in 2 years? 3 years? We've created guaranteed schedules to help make it happen.
YEAR ONE - Fall YEAR ONE - Spring
Full Term ENC1101 Full Term ENC1102 A Term B Term A Term B Term YEAR ONE - Fall YEAR ONE - Spring SLS1122 MGF2106 STA2023 SPC2608
Full Term ENC1101 Full Term ENC1102 YEAR ONE - Summer Elective A Term B Term A Term B Term
SLS1122 MGF2106 STA2023 SPC2608 YEAR TWO - Fall YEAR TWO - Spring Elective Elective Elective Elective Full Term Natural Science Full Term Natural Science A Term B Term A Term B Term
YEAR TWO - Fall YEAR TWO - Spring AMH2020/ ARH1000/ Social LIT2000 POS2041 MUL1010 Science Core Full Term Natural Science Full Term Natural Science A Term B Term A Term B Term YEAR TWO - Summer Elective
AMH2020/ ARH1000/ Social LIT2000 POS2041 MUL1010 Science Core YEAR THREE - Fall YEAR THREE - Spring Elective or Elective or Elective or Elective Full Term Elective Full Term Elective Language 1 Language 2 Cultural/ Global course A Term B Term A Term B Term
Elective or Elective or Elective or Elective Language 1 Language 2 Cultural/ Global course DaytonaState.edu/OnTime Why Students Should Take Face-To-Face Classes
Though students often take courses online because of the convenience, data shows that they do better in face-to-face courses. This is particularly true of math courses because of the assistance students get from their professors, in which explanations, proofs, and equations make more sense with the professor working out a problem with the student right there. When communicating through email or in a discussion forum, this help is watered down because of the time between a professor answering a question and when a student asks for further clarification. Professors can’t read non-verbal clues indicating a lack of understanding through email or through online discussions.
Students also benefit from face-to-face courses because they are required to work through problems without using the book or other materials as a crutch. This helps build their critical thinking skills, which will help them be more successful in later courses.
To help our students better succeed in math, often by 10% or more, your help is needed to get them into face-to-face sections. Consider these statistics comparing the difference in success between face-to-face and online courses: Face-to-Face Completion Online Completion Rates By Course (2015-16) Rates By Course (2015-16)
of students taking MAT1033 of students taking MAT1033 71% Intermediate Algebra 68% Intermediate Algebra
of students taking MGF2106 of students taking MGF2106 80% Survey in Mathematics 75% Survey in Mathematics
of students taking MGF2017 of students taking MGF2017 82% Liberal Arts Mathematics 73% Liberal Arts Mathematics
of students taking MAC1105 of students taking MAC1105 81% College Algebra 71% College Algebra
of students taking STA2023 of students taking STA2023 71% Elementary Statistics 62% Elementary Statistics Frequently Asked Questions about MAT1033 Intermediate Algebra, MAC1105 College Algebra, MGF2107 Liberal Arts Mathematics and MGF2106 Survey in Mathematics
1. Do I receive college credit for MAT1033 or MAT1033A?
Yes. These classes both count as elective credit toward an Associate of Arts degree. Although they do not satisfy the general education math requirements for associate degree programs, they provide a solid foundation for students who need to take MAC1105 - College Algebra for their majors. Please consult an academic advisor to determine how MAT1033 might apply to your program of study.
2. Can I take College Algebra MAC1105 after I have taken MAT0028?
No. If you want to take MAC1105, you’ll either need to earn a high enough score on the PERT mathematics test, or complete MAT1033 or MAT1033A with a grade of “C” or better.
3. If I take MGF2106, what Math class should I take next?
If you receive a C or better in MGF2106, then you are eligible to take STA2023 and MGF2107.
4. Which course is easier, MAT1033 or MGF2106?
MGF2106 deals with more “real world” applications of mathematics, and is appropriate for students entering many fields. The class is a computer-based course that includes some basic algebra, logic, reasoning, geometry, stats, and finance. MAT1033 is an algebra course that prepares students with the mathematics skills needed to move on to MAC1105, MAC1140, MAC1114, and MAC2311, which are required for many science, technology, and engineering programs.
5. What happens if I take MGF2106 but my program requires MAC1105 College Algebra?
In order to take MAC1105, you have to be eligible based on placement scores or take MAT1033 or MAT1033A and receive a grade of “C” or better prior to taking MAC1105.
6. Do I have computer work in MGF2106?
Yes. The course is based on projects and computer-based homework.
7. Do I have computer work in MAT1033?
Yes. The depth of computer work is based on whether you are taking online, hybrid, or face-to-face sections. Regardless of the modality, Falcon Online is used in all math classes. For specifics, you should contact your instructor.
8. I am taking MAT1033 now, but my program does not require MAC1105, which course should I take next?
If your program does not require MAC1105, the recommendation is to take MGF2106.
9. Can I take STA2023 after MGF2107?
No. To be eligible to take STA2023, you must earn a “C” or better in either MGF2106 or MAC1105. Should you take MAT1033 or MGF2106?
Does your major require MAC1105? Yes–take MAT1033 No–take MGF2106
How are these courses different? See table below
MAT1033 MGF2106 Intermediate Algebra Survey in Mathematics
MAT1033 does not fulfill the general MGF2106 does fulfill the general education mathematics requirement, but education mathematics requirement. counts as an elective. MAT1033 prepares you for the next MGF2106 prepares you for the next course in the STEM sequence . course in the non-STEM sequence. MAT1033 is the prerequisite for MGF2106 is a prerequisite for MAC1105 College Algebra. STA2023 Statistics. MAT1033 course grade is based on MGF2106 grades are based on quizzes, projects, homework and tests. attendance, projects and computer-work. Delivery modalities include Delivery modalities include face-to-face and online. face-to-face, hybrid and online.
How are these courses the same? Both are prerequisites for taking other college-credit mathematics courses. What is the students major? Use this guide to determine which mathematics courses are required for their major
Non-STEM Pathway
Accounting Technology Bachelor of Applied Science (BAS) Broadcast TV Production Business Administration Child Care Elementary/Exceptional Education Healthcare & Health Services Hospitality & Culinary Management Humanities Human Services Industrial Management Technology Interactive Media Interior Design Music Production Nursing Photographic Design Public Safety Social & Behavioral Sciences
MGF2106* MGF2106* Survey in Mathematics Survey in Mathematics
STA2023 MGF2107* Elementary Statistics Liberal Arts Mathematics
(Required for some majors) *MGF2106 and MGF2107 can be taken in any order STEM Pathway
Business Engineering Mathematics Science Secondary Education Technology
MAT1033 Intermediate Algebra
MAC1105 College Algebra
STA2023 Elementary Statistics
Business Degree STEM Degree
MAC1140 MAC1140* Pre-Calculus Algebra Pre-Calculus Algebra
MAC2233 MAC1114* Business Calculus Trigonometry
*MAC1140 and MAC1114 can be taken in any order MAC2311C or simultaneously Calculus I
MAC2312C Calculus II
MAC2313C Calculus III Study Guide Introduction
Because of the cumulative nature of mathematics, current knowledge of prerequisite skills and concepts greatly increases a student's opportunity for success in mathematics courses. Our goal is to help students succeed the first time they enroll in a mathematics course. Assessment of what they currently know is a very important part of helping students succeed.
We also understand that while students might have successfully completed a particular mathematics course, some of the necessary skills and concepts needed might be a bit rusty. So, we have put together a sample study guide for each course. We hope that by completing these 5 to 7 problems in the study guide, it will not only give the student a true picture of their current level of knowledge of a course, but also help us determine the best placement for the student. This will help the student be ready to learn new concepts when the student does enroll in the right mathematics course.
Student success matters from start to finish. They may require additional assistance outside of the classroom, and the School of Mathematics is here to help. They can take advantage of the following services: • Faculty Office Hours – Instructors hold 10 office hours every week. Instructors often answer the questions from the students through email, phone and in person.
• Supplemental Instruction (SI) – Looking for a review of the class material covered during the week? SI provides a weekly review session led by a peer who has previously taken the course and can provide a deeper understanding of the course material as well as effective study skills. Current courses supported by SI include: MAT1033 Intermediate Algebra, MAC1105 College Algebra, STA2023 Statistics, MAC1114 Trigonometry and MAC2311C Calculus I.
• Tutoring – One-on-one tutoring is provided through the Academic Support Center on all campuses. Students can simply walk in and ask a question. Tutors will assist in finding resources, clarifying class content, explaining assignments and offereing study suggestions. MAT0028 Study Guide (Solutions on pg. 18–19)
If you can answer these questions correctly, you are prepared to take MAT0028.
8 3 4 1. Add or subtract as indicated: + – 15 20 45 5 3 2. Add the mixed numbers by using improper fractions. 7 + 3 6 5
1 3. Alexa won a legal settlement for $418,500. Her lawyer received of the settlement. 3 a. How much money did the lawyer get? b. How much money did Alexa get?
0.8 4 4. Solve the proportion. = 3.1 p
5. Suppose a professional golfer who is ranked 10th in the world on the PGA Tour earns $2,183,000 per year. He pays his coach $185,000 per year. What percent of his income goes toward his coach? Round your answer to the nearest tenth of a percent.
13 MAT1033 Study Guide (Solutions on pg. 20–21)
If you can answer these questions correctly, you are prepared to take MAT1033.
1. Simplify (2a + 3b – 7) – 4(-5a – 6b + 12)
2. Which of the ordered pairs is a solution to the equation 2x – 3y = 7 a. (2, 1) b. (-1, -3)
3. Find the slope of a line passing through the points (-4, -2) and (6, -9)
4. Convert 282,000 to scientific notation. -5(6) 5. Simplify -3(-6) – 8
6. Solve 3t – 6 + 12t = 12 + 24t – 3
14 MAC1105 Study Guide (Solutions on pg. 22–23)
If you can answer these questions correctly, you are prepared to take MAC1105.
1. Find the domain of f(x) = x – 5
2. Write the equation of the line below:
3. Factor 3x2 – 14x – 24
4. Solve the following system and state the value of x
x = -3y + 1 2x + 4y = 12
5. Solve x2 + 6x + 5 = 0 10 3 6. Solve – 4 = x + 1 x + 1
7. Solve -2x + 5 ≥ 11 and write your answer in interval notation.
15 MAC1140 Study Guide (Solutions on pg. 24–27)
If you can answer these questions correctly, you are prepared to take MAC1140.
1. Use the quadratic formula to solve 9x2 – 6x – 4 = 0.
2. Find the difference quotient for the function f(x) = -x2 + x – 2 and then simplify.
3. The cost of a plastic sewer pipe varies jointly as its diameter and length. If a 20 foot pipe with a diameter of 6 inches costs $18.60, then what is the cost of a 16 foot pipe with a diameter of 8 inches?
4. Find the vertex of the quadratic function f(x) = 3x2 – 12x + 1
5. The sum of the three numbers is 40. The difference between the largest and smallest is 12, and the largest is equal to the sum of the two smaller numbers. Find the numbers.
16 MGF2106 Study Guide (Solutions on pg. 28–30)
If you can answer these questions correctly, you are prepared to take MGF2106. 3 5 1. Add and write your answer as a mixed number in simplest form. + 5 4 6 2. Solve for v. Simplify your answer as much as possible. 2(v + 5) = -2(8v – 3) + 4v
3. Use substitution to solve the system -5x + 3y = -35 3y + 19 = x
4. A TV has a listed price of $636.99 before tax. If the sales tax rate is 9.75%, find the total cost of the TV with sales tax included. Round your answer to the nearest cent, as necessary.
5. Find the volume of the rectangular prism.
1 6. Consider the equation y = - x + 3 3
a. Is (3, 2) a solution to the above equation. b. Graph the above equation.
17 MAT0028 Study Guide Solutions
1. First, we find the least common denominator (LCD) by factoring each denominator:
15 = 3 * 5
20 = 2 * 2 * 5
45 = 3 * 3 * 5 The LCD is 2 * 2 * 3 * 3 * 5 = 180. We convert each fraction to an equivalent fraction having a denominator of 2 * 2 * 3 * 3 * 5. We accomplish this by multiplying the numerator and the denominator of each original fraction by the factors missing from the denominator:
8 * 2 * 2 * 3 3 * 3 * 3 4 * 2 * 2 – + 3 * 5 * 2 * 2 * 3 2 * 2 * 5 * 3 * 3 3 * 3 * 5 * 2 * 2 We now combine the numerators and then simplify our answer to lowest terms.
96 – 27 + 16 85 5 * 17 17 = = = 180 180 36 * 5 36 17 Thus the final answer is 36
2. We write each mixed number as an improper fraction:
5 3 47 18 7 + 3 = + 6 5 6 5
Note that the LCD is 30. 47 18 47 * 5 18 * 6 235 108 343 + = + = + = 6 5 6 5 5 6 30 30 30 * * We will now use division to convert the improper fraction to a mixed number 13 343 ÷ 30 = 11 + 30 13 The result is 11 30 1 3. (a) We need to find what is of $418,500. We have, 3
1 418,500 (3 * 139,500) * $418,500 = = = 139,500 3 3 3 (b) Alexa will get what remains of the $418,500 after the lawyer gets his cut:
$418, 500 – $139, 500 = $279, 000. Alexa gets $279,000. 18 4. Set cross products equal to one another
0.8p = 3.1 * 4
Simplifying the RHS, we get
0.8p = 12.4
Dividing both sides by 0.8, we have p = 15.5
5. We want to find what percent of 2,183, 000 is $185, 000. Letp be the percent of the golfers earnings that goes to his coach. We have, 185,000 p = 2,183,000 100
The ratio on the right hand side (RHS) can be simplified by a factor of 1000. Strike through three zeros in the numerator and the denominator.
185 p = 2,183 100
Set the cross products to equal one another
185 * 100 = 2,183p
Simplifying the RHS, we get
18,500 = 2,183p
Divide both sides by 2,183 18,500 2,183p = 2,183 2,183 Simplifying the RHS we get 18,500 = p 2,183 Simplifying the LHS, we get 8.47 = p
The golf pro spends about 8.5% of his earnings on his coach.
19 MAT1033 Study Guide Solutions
1. Removing parentheses and changing signs, we get
2a + 3b – 7 + 20a + 24b – 48
Now we combine all like terms, we get 2a + 20a + 3b + 24b – 7 + 48 = 22a + 27b – 55
2. We are going to substitute the values of x and y into the equation: a. For (2, -1) we have 2(2) – 3(-1) = 4 + 3 = 7, so that makes the equation true. b. For (-1, -3) we have 2(-1) – 3(-3) = -2 + 9 = 7, so that makes the equation true.
3. For the slope
y2 – y1 m = x2 – x1
-9 – (-2) = 6 – (-4) -9 + 2 = 6 + 4
7 = - 10
4. We have 2.82 * 105
5. In simplifying, we have -5(6) -30 = -3(-6) – 8 18 – 8 -30 = 10 = -3
20 6. Combining like terms, we get 3t + 12t – 6 = 24t + 12 – 3
15t – 6 = 24t + 9. Subtracting 9 on both sides
15t – 9 – 6 = 24t + 9 – 9
15t – 15 = 24t. Subtracting 15t on both sides
15t – 15 – 15t = 24t – 15t. Upon simplifying the RHS and LHS, we get
-15 = 9t. Dividing both sides by 9
15 – = t. Simplifying the RHS we get 9 5 – = t 3
21 MAC1105 Study Guide Solutions
1. Since you cannot take the square root of a negative number because the result would yield an imaginary number, the domain is restricted to taking the square root of a positive number. So set the portion inside the square root x – 5 ≥ 0. Add 5 to both sides, we get x ≥ 5. The solution set is [5, ∞).
2. Looking at the graph the y-intercept is (0, 1) and the x-intercept is (2, 0). Using the slope formula
y2 – y1 1 – 0 1 m = = = - x2 – x1 0 – 2 2
1 Now, the slope intercept form of the line is y = mx + b. So y = - x + 1, and the y intercept is (0, 1). 2
3. Using the trial and error method, use factors of 3 and -24 that will sum to -14. We will have 2 binomials (3xa)(xb), we have no choice with the factors of 3, so we are looking at the factors of 24. With repeated attempts we get (3x + 4)(x – 6). Notice the middle term, 4x – 18x, sums to –14x.
4. Set up the equations in standard form of a line
(1) x + 3y = 1, (2) 2x + 4y = 12,
We are going to solve the equation for x by eliminating y. Multiply (1) by -4 and (2) by 3. So you have -4x – 12y = -4 6x + 12y = 36
Notice the ys are eliminated when adding the resulting equations. So you have
2x = 32. Dividing both sides by 2, we get 2x 32 = . Upon simplification, we get 2 2 x = 16
22 5. We are going to solve the quadratic equation by factoring. We have 2 binomials (using trial and error): (x + 5) (x + 1) = 0. Notice the sum of the factors of 5 and 1 add to 6, which is the middle factor of the quadratic equation. Set x + 5 = 0 and set x + 1 = 0, which yields x = -5 and x = -1.
6. The LCD is x + 1 for the equation. Notice x cannot be equal to -1, since that results in dividing by zero. Multiplying each term of the equation by x + 1, we get
10 – 4(x + 1) = 3. Distributing 4, we get
10 – 4x – 4 = 3. Combining like terms, we get
-4x + 6 = 3. Subtracting 6 on both sides, we get
-4x = -3. Dividing both sides by -4, we get 3 x = . 4
7. Solving for x, we first subtract 5 from each side
-2x ≥ 11 – 5. Upon simplifying the RHS, we get
-2x ≥ 6. Dividing both sides by -2
x ≤ -3
We switch the inequality because we divide by a negative number. In interval notation it is (-∞, -3].
23 MAC1140 Study Guide Solutions
1. We want to solve
9x2 – 6x – 4 = 0
Notice that this quadratic equation is already in standard form: ax2 + bx + c = 0 and we can identify a, b, and c:
a = 9, b = -6, c = -4
Recalling the quadratic formula
-b ± b2 – 4ac x = 2a
We will substitute for a, b, and c:
-(-6) ± (-6)2 – 4(9)(-4) x = 2(9) Upon simplifying, we have,
6 ± 36 + 144 6 ± 180 6 ± 36 * 5 6 ± 6 5 1 ± 5 x = = = = = 18 18 18 18 3 Thus the solution set is
1 + 5 1 – 5 , 3 3
2. Recall that the difference quotient is given by
f(x + h) – f(x)
h In the expression above we replace f(x + h) with the quantity
-(x + h)2 + (x + h) – 2
and then subtract the function f(x) = -x2 + x – 2:
-(x + h)2 + (x + h) – 2 – (-x2 + x – 2) h
24 MAC1140 Study Guide Solutions
If we expand the quantity (x + h)2 we obtain x2 + 2xh + h2:
-(x2 + 2xh + h2) + (x + h) – 2 – (-x2 + x – 2)
h Using the distributive property yields -x2 – 2xh – h2 + x + h – 2 + x2 – x + 2
h
We will now combine like terms -2xh – h2 + h
h
Upon dividing both the numerator and the denominator by h we obtain -2x – h + 1.
3. There is a direct variation problem, which means that the equation we will be using is
C = kdl
where C is the cost of the sewer pipe, k is the constant variation, d is the diameter of the pipe, and l is the length of the pipe.
We will first use the information in the problem to find the constant of variation
$18.60 = k(6)(20)
Solving for k yields k = 0.155. We now substitute for k: C = 0.155dl
So, the cost of a 16-foot pipe with a diameter of 8 inches is
C = 0.155(8)(16) = 19.84
The cost of the pipe is $19.84.
25 MAC1140 Study Guide Solutions
4. Recall that the vertex form of a quadratic function is
f(x) = a(x – h)2 + k,
where the vertex is given by (h, k). In the given problem a = 3, b = -12 and c = 1. The value of h is computed as demonstrated below.
b h = - 2a -12 = - . Simplifying the numerator and denominator, we get 2 * 3
12 = . Simplifying the fraction, we get 6
= 2.
The value of k is computed as demonstrated below.
4ac – b2 k = 4 ac (4 * 3 * 1) – (-12)2 = . Simplifying the numerator and denominator, we get 4 * 3 12 – 144 = . Simplifying the numerator again, we get 12
-132 = . Simplifying the fraction, we get 12
= -11
Thus the vertex is (2, -11)
26 5. Let x be the smallest of the three numbers and let z be the largest of the three numbers and let y be the middle number. Since the sum of the three numbers is 40, we have the equation:
x + y + z = 40
Since the difference between the largest and smallest is 12, we have the equation
z – x = 12
Since the largest is equal to the sum of the two smaller numbers, we have the equation
z = x + y
Thus we have the system x + y + z = 40
z – x = 12
z = x + y Substituting x + y = z in the first equation, we get z2 = 40. Dividing both sides by 2, we get z = 20. Substituting z = 20, in the second equation to obtain the value of x:
20 – x = 12. Subtracting 20 on both sides, we get -x = -8. Dividing both sides of the equation by -1, we get
x = 8
Substituting z = 20 and x = 8, to obtain the value of y: 20 = 8 + y. Subtracting 8 on both sides
12 = y.
Thus, x = 8, y = 12, and z = 20. The three numbers are 8, 12, and 20.
27 MGF2106 Study Guide Solutions
3 5 1. We first rewrite and 5 so they have a common denominator. We will use the LCD, 12. 4 6
3 9 = 4 12 5 10 5 = 5 6 12
Now we can do the addition. 9 10 19 + 5 = 5 12 12 12
Then we rename this answer.
19 19 7 7 5 = 5 + = 5 + 1 = 6 12 12 12 12
2. We can solve the equation as follows: 2(v + 5) = -2(8v – 3) + 4v. Using the distributive property to remove parentheses 2v + 10 = -16v + 6 + 4v. Combining like terms on each side 2v + 10 = -12v + 6. Subtracting 10 from each side 2v = -12v – 4. Adding 12v to each side 14v = -4, Dividing each side by 14
4 v = - . Upon simplification, we get 14 2 v = - . 7
28 3. Substituting 3y + 19 = x in -5x + 3y = -35 we get
-5(3y + 19) + 3y = -35. Distributing -5 on the LHS, we get
-15y – 95 + 3y = -35. Combining the like terms on the LHS, we get -12y – 95 = -35. Subtracting 95 on both sides, we get -12y = 60. Dividing both sides by -5, we get y = -5
To findx , we substitute y = -5 in 3y + 19 = x and get 3(-5) + 19 = x. Multiplying 3 with -5, we get -15 + 19 = x. Simplifying the terms on RHS, we get 4 = x
4. The sales tax is 9.75% of $636.99, and we calculate it as follows. First, we change 9.75% to a decimal by dividing 9.75 by 100.
9.75 9.75% = = 0.0975 100 Then, we multiply
9.75% of 636.99 = 0.0975 * 636.99
= 62.106525
Rounding to the nearest cent, we get that the sales tax is $62.11. To find the total cost, we add the listed price and the sales tax.
636.992 + 62.11 = 699.10
So, the total cost is $699.10
29 MGF2106 Study Guide Solutions
5. The volume V of a rectangular prism with length l, width w and height h is computed as follows.
V = l * w * h
In this problem, l = 5m, w = 5m, and h = 5m. So we get the following.
V = 5 * 5 * 5 = 125m3. For volume, the unit must be a 3rd power.
1 6. Consider the equation y = - x + 3. 3
a. We are going to substitute the values of x and y into the equation. For (3, 2) we have 1 - * 3 + 3 = -1 + 3 = 2, so that makes the equation true. 3 b. We need at least two points to graph the line. First, we choose some x values. Then, we 1 evaluate y = - x + 3 for each of the x values. 3
1 x y x x y = - 3 + 3 ( , )
1 0 y = - 0 + 3 = 3 (0, 3) 3 *
1 y 3 = - 3 * 3 + 3 = 2 (3, 2) 1 6 y = - 6 + 3 = 1 (6, 1) 3 *
30 Notes Contact Information Marc D. Campbell Barry Gibson Chairperson, School of Mathematics Assistant Chairperson, School of Mathematics Phone: (386) 506-3520 or (386) 506-3695 Phone: (386) 506-3122 Email: [email protected] Email: [email protected]
Gail Beckwith Administrative Assistant, School of Mathematics Phone: (386) 506-3695 Email: [email protected]
DaytonaState.edu A MEMBER OF THE FLORIDA COLLEGE SYSTEM Daytona State College is an equal opportunity institution. 104178K_061 01/19 Math Pathways video: https://youtu.be/31MWZDFs8pI